Jha had been detained since Saturday for interrogation in connection with the probe into the Class 12 toppers scam case by the SIT.
"SIT has finally arrested Jha on the basis of revelations made by him and others arrested," a police official said.
The SIT will produce him in the local court later Monday.
Last week SIT arrested the board's former chairman Lalkeshwar Prasad and his wife and former Janata Dal-United legislator Usha Sinha from Varanasi in Uttar Pradesh. Both are lodged in Beur jail here.
Earlier, SIT arrested Bachcha Rai, alleged kingpin of the scam. Rai is director-cum- principal of V.R. College in Vaishali district. He is also in jail.
SIT has already arrested Class 12 'topper' in Arts, Rubi Rai, who had said political science is all about cooking, after she failed in a re-test. Her result was also cancelled.
So far, nearly 20 persons have been arrested in the case, the police said.
The scam surfaced after Aaj Tak TV channel showed a sting in which two Class 12 toppers were unable to answer even elementary questions about the subjects they 'topped' in.
The sting showed Rubi Rai, who topped the Class 12 exam in Arts, saying: "Prodikal (read political) science is about cooking."
It also showed Saurabh Shreshtha, a Science topper, saying: "Most reactive element in the periodic table is aluminium."
Both Rubi Rai and Saurabh Shreshtha belonged to Bachha Rai's V.R. College.
The sting suggested that education in Bihar continues to be a very dubious affair with cheating and fraud apparently continuing on a large scale.